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Changing delayed formula
*To*: mathgroup at smc.vnet.net
*Subject*: [mg35461] Changing delayed formula
*From*: "Julio Vera" <jvera at adinet.com.uy>
*Date*: Sat, 13 Jul 2002 03:49:01 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
Hi,
I have a list of lists. it's length (the number of sublists it
contains) varies.
In[1]:= des={{11,12,13,14},{21,22,23},{31,32},{41,42,43,44,45}}
Out[1]:= {{11,12,13,14},{21,22,23},{31,32},{41,42,43,44,45}}
The length of each of the sublists is arbitrary, too. So I have this
list of lengths.
In[2]:= elems=Flatten[Table[Dimensions[des[[i]]],{i,Length[des]}]]
Out[2]:= {4,3,2,5}
I want to obtain the list of all combinations of one element of each
sublist, bounded by &&. This will be a list of 120 elements, each of
them with 4 components. I define a delayed formula, and apply Array to
it (the characters printed as bold are subscripts in the Mathematica
notebook).
In[3]:=
cond4[a_,b_,g_,d_]:=des[[1,a]]&&des[[2,b]]&&des[[3,g]]&&des[[4,d]]
In[4]:= combi=Flatten[Array[condLength[des],elems]]
Out[4]:=
{11&&21&&31&&41,11&&21&&31&&42,11&&21&&31&&43,11&&21&&31&&44,...
...14&&23&&32&&42,14&&23&&32&&43,14&&23&&32&&44,14&&23&&32&&45}
Since the length of des varies, I would have to define cond each time.
For instance:
cond3[a_,b_,g_,d_]:=des[[1,a]]&&des[[2,b]]&&des[[3,g]]
I would like to make a definition for cond that would adapt to these
changes automatically.
I arrived to this solution, which is not rejected by Mathematica, but
does not work, either.
In[5]:= d[a_,b_]:=des[[a,b<>"_"]]
In[6]:= Unprotect[ReplaceAll]
Out[6]:= {ReplaceAll}
In[7]:=
condLength[des][Table[FromCharacterCode[944+i]<>"_",{i,Length[des]}]]/.{a__}=AEa:=Apply[And,Table[d[i,FromCharacterCode[944+i]<>"_"],{i,Length[des]}]]
In fact, I quit the kernel and rerun all the cells except the one
written here as In[3]. If not, the definition for cond4 remains as it
was. I was not able to clear cond4 individually.
Thanks very much for anything you can suggest.
Best regards,
Julio Vera
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